Self-adjoint extension approach to the spin-1/2 Aharonov-Bohm-Coulomb problem

Abstract

The spin-1/2 Aharonov-Bohm problem is examined in the Galilean limit for the case in which a Coulomb potential is included. It is found that the application of the selfadjoint extension method to this system yields singular solutions only for one-half the full range of flux parameter which is allowed in the limit of vanishing Coulomb potential. Thus one has a remarkable example of a case in which the condition of normalizability is necessary but not sufficient for the occurrence of singular solutions. Expressions for the bound state energies are derived. Also the conditions for the occurrence of singular solutions are obtained when the non-gauge potential is ξ/r p (0 ≤ p < 2).

On the quantum dynamics of a point particle in conical space

“…However, the self-adjoint extension approach is a more direct procedure to find the physics compatible with shortranged potentials. The reader can compare, for example, the Aharonov-Bohm-Coulomb problem discussed by Hagen and Park [5] and by Park and Oh [23]. The same non-relativistic spectrum was achieved in both articles but with much less work in the second, where the self-adjoint extension was used.…”

Relativistic quantum dynamics of a neutral particle in external electric fields: An approach on effects of spin

“…The AC effect and consequently the AB effect also has been addressed to bound states. In the context of the method of operators in quantum mechanics such bound states are found by modeling the problem by boundary conditions at the origin [12][13][14][15][16][17][18][19][20][21][22][23] (See also Refs. [24][25][26][27] where bound states also are obtained for Aharonov-Bohm-like systems.…”

The second virial coefficient of spin- interacting anyon system

“…Furthermore, the probability of the overlap of two particles is always zero. This property is also valid for spin-1/2 system with the same two-particle interaction [10]. They showed that this simple interaction makes the cusps at bose points smooth for spinless case.…”